The title won't do justice with what i want to ask so let me put forth scenario. I studied and i have researched that it is a established and well supported theory that space and time did not exist before big bang. We know all forms of energy even the electromagnetic energy requires space and time to exhibit itself. To sum up we need at least space or time or both for energy to exhibit itself. But when we talk about quantum vacuum. They say it is analogous to nothing as the vacuum contains very low energy and hence it is nothing and we can create something out of nothing. But there is space,time and energy as well. How come it is nothing when there exists everything needed to prepare the recipe of the matter. Moreover, i heard about a theory, that this quantum vacuum can explain how big bang happened. How everything came out of nothing. But space and time came after Big Bang and this quantum vacuum which according to me requires space,time and energy
You are correct that "quantum vacuum" usually presupposes space and time. Usually it refers to the lowest-energy state of a set of quantum fields.
However, in "quantum cosmology" there are attempts to apply quantum concepts to the entire universe. For example, quantum mechanics can give you the probability to go from one state to another state, in a way that involves summing over possible intermediate states.
In some forms of quantum cosmology, such probability sums are constructed, that start with true nothingness - not even space or time - and end with something like the early universe (as known in observational cosmology) or the universe today.
This is mathematically possible because of how space and time are described in modern theories of gravity. Rather than the universe being an eternal Euclidean space, such as Galileo or Newton may have assumed, space and time themselves are described as a four-dimensional "manifold" which can "curve" (in a new sense of that word, introduced by Riemann); which can be finite in size; and which can expand from a point, starting at a finite time in the past.
The probability sum which tells you the odds of starting with "nothing" and arriving at "a universe like the present", is then something like a sum over all those possible universes that start at a point and expand to become like the universe we see. I say it's "something like" that sum, because (1) the universe may be described in an extremely simplified fashion (see minisuperspace), e.g. it might be described by just one number, its "radius of curvature" (2) the sum often involves mathematical tricks, like allowing that "radius" to be a complex number, which is inconsistent with the geometrical interpretation of its meaning.
Quantum cosmology is full of mathematics generalized beyond its original physical interpretation, to which theoretical physicists may then attach peculiar or dubious meanings, in an attempt to explain to themselves what their equations mean. Hawking and Vilenkin are perhaps the most influential authors of theories in which the quantum universe somehow comes from nothing, but dozens of other people have tried inventing their own versions (random example).
Summing up :-) ... If someone talks about the universe coming from a quantum vacuum before space and time, they are trying to make a conceptual theory about the meaning of their mathematical theory of the quantum universe. It's hard to be any more specific, because the details are often idiosyncratic. But in general, there's no guarantee that the conceptual theory makes logical sense, or that the mathematical theory has anything to do with the actual universe.